CTF3102 Logical Analysis and Problem Solving - University of Bolton

Learning Outcome 1: Apply mathematical techniques to perform calculations using given number systems

Learning Outcome 2: Use Logic Gates and Boolean logic to solve given problems supported by Truth Tables.

Learning Outcome 3: Apply statistical principles to discern meaningful information based on a given scenario.

Learning Outcome 4: Demonstrate the use of algebra to solve given problems

Section 1 Show all necessary calculations.

Question 1. Calculate the sum of 10₈ and 84₁₀. Show the result in hexadecimal.
Question 2. Subtract 101111₂ from11000011₂. Show the result in binary.
Question 3. Evaluate 4+3 × 7 using the BODMAS rule
Question 4. A foundation student bought a mobile phone and smart watch for a total of £1,250, excluding VAT (value added tax), paying 3 times as much for the mobile phone as for the smart watch.

a) Write an expression to show the total cost in terms of the cost of the smart watch.
b) What was the cost of each item?
c) Calculate the VAT on the mobile phone, assuming a VAT rate of 14%

Question 5. The pressure p in a reaction vessel changes from 169 Pascal to 54 Pascal. What is the Change in pressure?

Question 6. Calculate the value of a in the equation 14(2a - 4) = 2(a + 8)

Question 7. The figure below shows a logic circuit and its incomplete truth table. Use the logic circuit to complete the truth table (i.e. find the output Q).

Question 8. What is the result of simplifying the expression 19a + 8b -2c -4b - 6c + a?

Question 9. Consider the following:

An online trading company wants to offer discounts to new customers. The company has recently emailed discount code to the customers. New customer must have a discount code to be eligible but returning customer are not eligible for a discount.

Let

A = Returning Customer B = Discount Code

(a) Draw a truth table to represent when a customer has a discount.

(b) From your truth table in (a) produce a Boolean expression to represent discounted customer (Q) for the trading company.

Section 2

Question 10. The data below shows the monthly rent for 24 students: 1500, 1350, 350, 1200, 850, 900, 1500, 1150, 1500, 900, 1400, 1100, 1250, 600,610, 960, 890, 1325, 900, 800, 2550, 495, 1200, 690.
(a) Create a relative frequency distribution table using 7 classes

(b) Use your table in (a) to produce a histogram to represent your data

Question 11. The following is a frequency table showing the ages of members of a symphony orchestra for young adults.

Age   Frequency
15            2
16            5
17           11
18            9
19           14
20           13
21           10
22           13

Find the sample mean and median of the ages of the 77 members of the symphony. [3]

Section 3 [Flowchart and Algorithm Development]

Question 12 Given the following list of steps in the admission process:
a. Search for a school
b. Prepare for the admission test and write test
c. Did you pass the exam?
d. Submit necessary documents and get admission
e. End
f. Are seats available?
g. Start
h. Is there an admission test?

Re-arrange the above steps in the correct order and use MS Visio to draw a flowchart for the admission process.

Question 13. Given the lengths of three sides of a triangle as a, b, c. Draw a flowchart to determine if the triangle is Isosceles, Equilateral, or Scalene.

Hint: In an equilateral triangle three sides are equal. In an isosceles triangle two sides are equal. In a scalene triangle three sides are not equal.

Attachment:- Logical analysis and problem solving.rar